Evaluation of empirical mode decomposition for quantifying multi-decadal variations and acceleration in sea level records

Abstract. The ability of empirical mode decomposition (EMD) to extract multi-decadal variability from sea level records is tested using three simulations: one based on a series of purely sinusoidal modes, one based on scaled climate indices of El Nino and the Pacific decadal oscillation (PDO), and the final one including a single month with an extreme sea level event. All simulations include random noise of similar variance to high-frequency variability in the San Francisco tide gauge record. The intrinsic mode functions (IMFs) computed using EMD were compared to the prescribed oscillations. In all cases, the longest-period modes are significantly distorted, with incorrect amplitudes and phases. This affects the estimated acceleration computed from the longest periodic IMF. In these simulations, the acceleration was underestimated in the case with purely sinusoidal modes, and overestimated by nearly 100% in the case with prescribed climate modes. Additionally, in all cases, extra low-frequency modes uncorrelated with the prescribed variability are found. These experiments suggest that using EMD to identify multi-decadal variability and accelerations in sea level records should be used with caution.

[1]  Philip L. Woodworth,et al.  R. Player. . The Permanent Service for Mean Sea Level: An update to the 21st century. , 2003 .

[2]  D. Chambers,et al.  Anomalous warming in the Indian Ocean coincident with El Niño , 1999 .

[3]  T. Ezer,et al.  Is sea level rise accelerating in the Chesapeake Bay? A demonstration of a novel new approach for analyzing sea level data , 2012 .

[4]  John A. Church,et al.  Evidence for the accelerations of sea level on multi‐decade and century timescales , 2009 .

[5]  Mukti Fatimah,et al.  ANALISIS PERUBAHAN TINGGI MUKA AIR LAUT DI KOTA PADANG TAHUN 2008 SAMPAI 2012 DENGAN MENGGUNAKAN DATA PERMANENT SERVICE FOR MEAN SEA LEVEL (PSMSL) , 2013 .

[6]  L. Miller,et al.  Gyre‐scale atmospheric pressure variations and their relation to 19th and 20th century sea level rise , 2007 .

[7]  Peicai Yang,et al.  The prediction of non-stationary climate series based on empirical mode decomposition , 2010 .

[8]  N. Huang,et al.  A study of the characteristics of white noise using the empirical mode decomposition method , 2004, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[9]  Han Soo Lee.  Estimation of extreme sea levels along the Bangladesh coast due to storm surge and sea level rise using EEMD and EVA , 2013 .

[10]  P. Jones,et al.  An Extension of the TahitiDarwin Southern Oscillation Index , 1987 .

[11]  Gary Meyers,et al.  Multidecadal variations of Fremantle sea level: Footprint of climate variability in the tropical Pacific , 2004 .

[12]  N. Huang,et al.  Global sea level trend during 1993–2012 , 2014 .

[13]  Laurence C. Breaker,et al.  The 154-year record of sea level at San Francisco: extracting the long-term trend, recent changes, and other tidbits , 2011 .

[14]  Norden E. Huang,et al.  Ensemble Empirical Mode Decomposition: a Noise-Assisted Data Analysis Method , 2009, Adv. Data Sci. Adapt. Anal..

[15]  K. Wolter,et al.  Measuring the strength of ENSO events: How does 1997/98 rank? , 1998 .

[16]  S. Philander.  Our Affair with El Niño: How We Transformed an Enchanting Peruvian Current into a Global Climate Hazard , 2004 .

[17]  M. Karpytchev,et al.  Long‐term sea level trends: Natural or anthropogenic? , 2014 .

[18]  S. Holgate.  On the decadal rates of sea level change during the twentieth century , 2007 .

[19]  R. Steven Nerem,et al.  Is there a 60‐year oscillation in global mean sea level? , 2012 .

[20]  S. George Philander,et al.  Geophysical Interplays. (Book Reviews: El Nino, La Nina, and the Southern Oscillation.) , 1990 .

[21]  N. Bond,et al.  Recent shifts in the state of the North Pacific , 2003 .

[22]  A. Miller,et al.  Dynamical suppression of sea level rise along the Pacific coast of North America: Indications for imminent acceleration , 2011 .

[23]  N. Huang,et al.  The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis , 1998, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[24]  Tal Ezer,et al.  Gulf Stream's induced sea level rise and variability along the U.S. mid‐Atlantic coast , 2013 .

[25]  J. Wallace,et al.  ENSO-like Interdecadal Variability: 1900–93 , 1997 .

[26]  Gabriel Rilling,et al.  On empirical mode decomposition and its algorithms , 2003 .

[27]  G. Mitchum,et al.  An Anomalous Recent Acceleration of Global Sea Level Rise , 2009 .

[28]  J. Wallace,et al.  A Pacific Interdecadal Climate Oscillation with Impacts on Salmon Production , 1997 .

[29]  Christian Franzke,et al.  Nonlinear Trends, Long-Range Dependence, and Climate Noise Properties of Surface Temperature , 2012 .

[30]  B. C. Douglas,et al.  Wind effects on estimates of sea level rise , 2011 .

[31]  A. Müller,et al.  Evidence for long‐term memory in sea level , 2014 .

[32]  Christian Franzke,et al.  Multi-scale analysis of teleconnection indices: climate noise and nonlinear trend analysis , 2009 .

[33]  Norden E. Huang,et al.  A review on Hilbert‐Huang transform: Method and its applications to geophysical studies , 2008 .

[34]  D. Chambers,et al.  Quantifying recent acceleration in sea level unrelated to internal climate variability , 2013 .

[35]  Peter J. Kyberd,et al.  EMG signal filtering based on Empirical Mode Decomposition , 2006, Biomed. Signal Process. Control..

[36]  A. Vecchio,et al.  Natural periodicities and Northern Hemisphere–Southern Hemisphere connection of fast temperature changes during the last glacial period: EPICA and NGRIP revisited , 2014 .

[37]  Kevin E. Trenberth,et al.  Signal Versus Noise in the Southern Oscillation , 1984 .